Inducing anisotropies in Dirac fermions by periodic driving

Floquet engineering of topological phases is becoming increasingly popular. One particular example of great interest is that of Floquet topological insulators [1]. In our work, we consider the three-dimensional Hamiltonian for Bi₂Se₃, a second-generation topological insulator, under the effect of a periodic drive for both in-plane and out-of-plane fields. As it will be shown by means of high-frequency expansions up to second order in the Floquet Hamiltonian, the driving induces anisotropies in the Dirac cone and opens up a quasienergy gap for in-plane elliptically polarized fields. Analytic expressions are obtained for the renormalized velocities and the quasienergy gap [2]. These expressions are then compared to numerical calculations performed by discretizing the Hamiltonian in a one-dimensional lattice and following a staggered fermion approach [3], achieving a remarkable agreement. We believe our work may have an impact on the transport properties of topological insulators.

References
[1] M. S. Rudner and N. H. Lindner, Nat. Rev. 2, 229 (2020).
[2] A. Díaz-Fernández, J. Phys.: Condens. Matter 32, 495501 (2020).
[3] A. Díaz-Fernández, E. Díaz, A. Gómez-León, G. Platero, and F. Domínguez-Adame, Phys. Rev. B 100, 075412 (2019).